How can I render something like a lattice around my object?
As the lattice can not be rendered, you can use a mesh object with the same geometry and hook both with empties.



In the example above, the lattice is the default cubic lattice which is associated via hooks to a simple cube. The cube itself has a wireframe modifier.

The recipe:


Create the lattice and the cube so that they have the same initial geometry
Add a wireframe modifier to the cube
Now create the hooks for the cube :
Enter edit mode, select a vertex
Use CtrlH to make the hook menu appear and choose "hook to new object"
Do that for all the vertices of the cube
Once done come back to object mode
Now the lattice part:
Select the lattice and enter to edit mode
Select a vertex 
Use CtrlH and choose "assign to hook" and choose the corresponding previously created empty
Do that for all the vertices of the lattice


Note: if you have many (say more than 8) vertices to manipulate, it can be difficult to remember which empty correspond to which vertex. So you can also do the following:


In object mode, select the empty the shift select the lattice
Enter edit mode
Select the corresponding vertex
Use CtrlH but now choose "hook to selected object"
Come back in object mode and do the same for the other empties/vertices